The isomonodromic connection \(\hat{\alpha }\)  has (single-valued)
coefficients which are holomorphic for \(\lambda \in \ast \) ,
but has poles of order 2 at \(\lambda =0\)  and \(\lambda =\infty \) .
Its monodromy data consists of Stokes matrices relating solutions on sectors
at each pole and “connection matrices” relating solutions at \(\lambda =0\)  and \(\lambda =\infty \) .
We refer to chapter 1 of [1]} for these concepts from o.d.e. theory.
